Problem: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{4}{15}-8\dfrac{2}{4} = {?}$
Simplify each fraction. $= {12\dfrac{4}{15}} - {8\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {12\dfrac{8}{30}}-{8\dfrac{15}{30}}$ Convert ${12\dfrac{8}{30}}$ to ${11 + \dfrac{30}{30} + \dfrac{8}{30}}$ So the problem becomes: ${11\dfrac{38}{30}}-{8\dfrac{15}{30}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{38}{30}} - {8} - {\dfrac{15}{30}}$ Bring the whole numbers together and the fractions together: $= {11} - {8} + {\dfrac{38}{30}} - {\dfrac{15}{30}}$ Subtract the whole numbers: $=3 + {\dfrac{38}{30}} - {\dfrac{15}{30}}$ Subtract the fractions: $= 3+\dfrac{23}{30}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{23}{30}$